Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time \(t_1\). On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time \(t_2\). The time taken by her to walk upon the moving escalator will be:
1. \(\frac{t_1t_2}{t_2-t_1}\)
2. \(\frac{t_1t_2}{t_2+t_1}\)
3. \(t_1-t_2\)
4. \(\frac{t_1+t_2}{2}\)
The coordinate of an object is given as a function of time by , where x is in metres and t is in seconds. Its average velocity over the interval t=0 to t=4 is will be:
1. 5 m/s
2. -5 m/s
3. 11 m/s
4. -11 m/s
A particle moves along a straight line and its position as a function of time is given by\(x= t^3-3t^2+3t+3\)
1. | \(t=1~\text{s}\) and reverses its direction of motion | stops at
2. | \(t= 1~\text{s}\) and continues further without a change of direction | stops at
3. | \(t=2~\text{s}\) and reverses its direction of motion | stops at
4. | \(t=2~\text{s}\) and continues further without a change of direction | stops at
If the velocity of a particle is \(v=At+Bt^{2},\) where \(A\) and \(B\) are constants, then the distance travelled by it between \(1~\text{s}\) and \(2~\text{s}\) is:
1. | \(3A+7B\) | 2. | \(\frac{3}{2}A+\frac{7}{3}B\) |
3. | \(\frac{A}{2}+\frac{B}{3}\) | 4. | \(\frac{3A}{2}+4B\) |
A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to where and \(\mathrm{n}\) are constants and \(\mathrm{x}\) is the position of the particle. The acceleration of the particle as a function of \(\mathrm{x}\) is given by:
1.
2.
3.
4.
A stone falls freely under gravity. It covers distances \(h_1,~h_2\) and \(h_3\) in the first \(5\) seconds, the next \(5\) seconds and the next \(5\) seconds respectively. The relation between \(h_1,~h_2\) and \(h_3\) is:
1. | \(h_1=\frac{h_2}{3}=\frac{h_3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \) |
2. | \(h_2=3h_1\) and \(h_3=3h_2\) |
3. | \(h_1=h_2=h_3\) |
4. | \(h_1=2h_2=3h_3\) |
A ball is dropped from a high-rise platform at t = 0 starting from rest. After 6 seconds, another ball is thrown downwards from the same platform with speed v. The two balls meet after 18 seconds. What is the value of v?
1. | 75 ms-1 | 2. | 55 ms-1 |
3. | 40 ms-1 | 4. | 60 ms-2 |
A particle moves in a straight line with a constant acceleration. It changes its velocity from \(10\) ms-1 to \(20\) ms-1 while covering a distance of \(135\) m in \(t\) seconds. The value of \(t\) is:
1. | 10 | 2. | 1.8 |
3. | 12 | 4. | 9 |
A car moves from \(\mathrm{X}\) to \(\mathrm{Y}\) with a uniform speed \(\mathrm{v_u}\) and returns to \(\mathrm{X}\) with a uniform speed \(\mathrm{v_d}.\) The average speed for this round trip is:
1.
2.
3.
4.
A particle moves along a straight line OX. At a time t (in seconds), the displacement x (in metres) of the particle from O is given by x= 40 + 12t – t3. How long would the particle travel before coming to rest?
1. | 24 m | 2. | 40 m |
3. | 56 m | 4. | 16 m |